The window "Domain" displays a domain (as a wireframe) and a point (u0, v0) in the domain.

The window "Surface X(u,v)" shows the cylinder X(u,v) = (cos(u), sin(u), v), the point X(u0, v0), and the tangent vectors Xu(u0,v0) and Xv(u0,v0) with their tails at that point.

The window "Projection" displays the projection of the surface X(u,v) onto the tangent plane at X(u0, v0).

The control window displays the four elements of the matrix g associated to the first fundamental form. Note that g11 gives the square of the length of Xu(u0,v0) (the red vector), g22 gives the square of the length of Xv(u0,v0) (the green vector), and g12 and g21 give the dot product of Xu(u0,v0) and Xv(u0,v0), which equals the product of the lengths of the two vectors times the cosine of the angle between them. It is possible to change u0 and v0 in the control window.